0-pi-2-ln-sin-x-sec-2-x-dx-

Question Number 140614 by bramlexs22 last updated on 10/May/21

\int_{0}^{\frac{π}{2}} \ln (\sin x) \sec^{2} x dx = ?

Answered by bemath last updated on 10/May/21

Answered by Dwaipayan Shikari last updated on 10/May/21

\int_{0}^{\frac{π}{2}} l o g (s i n x) {s e c}^{2} x d x

= {[l o g (s i n x) t a n x]}_{0}^{\frac{π}{2}} - \int_{0}^{\frac{π}{2}} t a n x . \frac{c o s x}{s i n x} d x

= 0 - \frac{π}{2} = - \frac{π}{2}